4-6
Formalizing Relations
and Functions
Vocabulary
Review
domain
1. Use the words below to label the function
machine at the right. Use each word once.
function rule
y-values
output
x-values
input
range
equation
Vocabulary Builder
reasonable (adjective) ree zun uh bul
Example: It is reasonable to expect warm weather in Miami in July.
Nonexample: It is not reasonable to expect snow in Miami in July.
Other Word Forms: reasonableness (noun); reasonably (adverb)
Opposite: unreasonable (adjective)
Use Your Vocabulary
Complete each sentence with the appropriate word from the list.
reasonable
reasonableness
unreasonable
2. The student estimated to check the 9 of her answer.
3. Sales tax of $32 on an $85 item is 9.
4. A price of $14 is 9 for a pizza.
Chapter 4
130
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
Definition: Something is reasonable if it makes sense or is sensible.
Problem 1 Identifying Functions Using Mapping Diagrams
Got It? Identify the domain and range of the following relation:
{(4.2, 1.5), (5, 2.2), (7, 4.8), (4.2, 0)}
Represent the relation with a mapping diagram. Is the relation a function?
5. Use the words domain and range to label the mapping diagram. Then draw arrows
to represent the relation.
0
1.5
2.2
4.8
4.2
5
7
6. Does the relation map each domain value to
exactly one range value?
Yes / No
7. Is the relation a function?
Yes / No
You can use the vertical line test to decide whether a relation is a function. If any
vertical line passes through more than one point of the graph, then the relation is not
a function.
Problem 2 Identifying Functions Using the Vertical Line Test
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
Got It? Is the relation {(4, 2), (1, 2), (0, 1), (22, 2), (3, 3)} a function?
Use the vertical line test.
8. Begin by graphing the points from the relation on the coordinate plane.
4
y
2
x
Ľ4
Ľ2
O
2
4
Ľ2
Ľ4
9. Can you draw a vertical line that intersects more than one point?
If so, draw it.
10. Is the relation a function?
Yes / No
Yes / No
131
Lesson 4-6
Problem 3 Evaluating a Function
Got It? The function w(x) 5 250x represents the number of words w(x) you can
read in x minutes. How many words can you read in 6 min?
11. You should substitute
for x.
12. The function is evaluated below. Write the justification for each step.
w(x) 5 250x
w(6) 5 250 ? 6
w(6) 5 1500
13. You can read
Problem 4
words in 6 minutes.
Finding the Range of a Function
Got It? The domain of g(x) 5 4x 2 12 is {1, 3, 5, 7}. What is the range?
14. Underline the correct word to complete each sentence.
The domain / range is the set of input values.
The domain / range is the set of output values.
g(1)
g(3)
g(5)
g(7)
16. The range of g(x) 5 4x 2 12 with domain {1, 3, 5, 7} is
{
,
,
,
}.
Problem 5 Identifying a Reasonable Domain and Range
Got It? You have 7 qt of paint to paint the trim in your house. A quart of paint
covers 100 ft 2 . The function A(q) 5 100q represents the area A(q), in square feet,
that q quarts of paint cover. What domain and range are reasonable for the function?
Chapter 4
132
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
15. Use the function g(x) 5 4x 2 12 with domain {1, 3, 5, 7}. Find each output.
17. Complete the reasoning model below.
Think
Write
The least amount of paint I can use is 0 qt.
A(
) â100 Ƃ
So, that is the least domain value.
A(
) â
The greatest amount of paint I can use is 7 qt.
A(
) â100 Ƃ
So, that is the greatest domain value.
A(
) â
18. A reasonable domain is
#q#
19. A reasonable range is
.
# A(q) #
.
Lesson Check • Do you UNDERSTAND?
Error Analysis A student drew the dashed line on the graph shown and
concluded that the graph represented a function. Is the student correct? Explain.
20. Describe how the vertical line test helps you decide whether a relation is
a function.
y
2
O
2
4
x
____________________________________________________________________
____________________________________________________________________
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
21. Underline the correct word or words to complete each sentence about the graph.
I can draw a vertical line that passes through only one point / more than one point .
Therefore the graph does / does not represent a function.
22. Describe the student’s error.
__________________________________________________________________________________
__________________________________________________________________________________
Math Success
Check off the vocabulary words that you understand.
relation
domain
range
vertical line test
function notation
Rate how well you understand functions.
Need to
review
0
2
4
6
8
Now I
get it!
10
133
Lesson 4-6
© Copyright 2024 ExpyDoc
